If limx→∞ 1+ax−4x22x=e3, then 'a' is equal to

A
$\frac{2}{3}$
B
$\frac{3}{2}$
C
2
D
$\frac{1}{2}$

Solution:

We have,

$\begin{array}{l} lim_{x \to \infty} {(1 + \frac{a}{x} - \frac{4}{x^{2}})}^{2 x} = e^{3} \\ \Rightarrow e^{lim_{x \to \infty} 2 x (\frac{a}{x} - \frac{4}{x^{2}})} = e^{3} \\ \Rightarrow lim_{x \to \infty} (2 a - \frac{8}{x}) = 3 \Rightarrow 2 a = 3 \Rightarrow a = \frac{3}{2} \end{array}$

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If $lim_{x \to \infty} {(1 + \frac{a}{x} - \frac{4}{x^{2}})}^{2 x} = e^{3},$ then $' a'$ is equal to

Solution:

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